I deal with machine learning and web graphs analysis (mostly in theory). I also work on the development of Big Data products for one of the mobile operators in Russia. It's the first time I write a post, so please, don't judge me too harshly. Nowadays, a lot of people want to develop efficient algorithms and take part in machine learning competitions. So they come to me and ask: "Where to start?".

I am using the from the wikipedia page to find the gradient descent. What will be gradient descent equation for this. And as for ridge regression if i am using very large data sets. Instead of calculating the inverse is there another way to calculate it.

In the biclustering problem, we seek to simultaneously group observations and features. While biclustering has applications in a wide array of domains, ranging from text mining to collaborative filtering, the problem of identifying structure in high dimensional genomic data motivates this work. In this context, biclustering enables us to identify subsets of genes that are co-expressed only within a subset of experimental conditions. We present a convex formulation of the biclustering problem that possesses a unique global minimizer and an iterative algorithm, COBRA, that is guaranteed to identify it. Our approach generates an entire solution path of possible biclusters as a single tuning parameter is varied. We also show how to reduce the problem of selecting this tuning parameter to solving a trivial modification of the convex biclustering problem. The key contributions of our work are its simplicity, interpretability, and algorithmic guarantees - features that arguably are lacking in the current alternative algorithms. We demonstrate the advantages of our approach, which includes stably and reproducibly identifying biclusterings, on simulated and real microarray data.

As an automatic method of determining model complexity using the training data alone, Bayesian linear regression provides us a principled way to select hyperparameters. But one often needs approximation inference if distribution assumption is beyond Gaussian distribution. In this paper, we propose a Bayesian linear regression model with Student-t assumptions (BLRS), which can be inferred exactly. In this framework, both conjugate prior and expectation maximization (EM) algorithm are generalized. Meanwhile, we prove that the maximum likelihood solution is equivalent to the standard Bayesian linear regression with Gaussian assumptions (BLRG). The $q$-EM algorithm for BLRS is nearly identical to the EM algorithm for BLRG. It is showed that $q$-EM for BLRS can converge faster than EM for BLRG for the task of predicting online news popularity.

We study the minimization of a convex function $f(X)$ over the set of $n\times n$ positive semi-definite matrices, but when the problem is recast as $\min_U g(U) := f(UU^\top)$, with $U \in \mathbb{R}^{n \times r}$ and $r \leq n$. We study the performance of gradient descent on $g$---which we refer to as Factored Gradient Descent (FGD)---under standard assumptions on the original function $f$. We provide a rule for selecting the step size and, with this choice, show that the local convergence rate of FGD mirrors that of standard gradient descent on the original $f$: i.e., after $k$ steps, the error is $O(1/k)$ for smooth $f$, and exponentially small in $k$ when $f$ is (restricted) strongly convex. In addition, we provide a procedure to initialize FGD for (restricted) strongly convex objectives and when one only has access to $f$ via a first-order oracle; for several problem instances, such proper initialization leads to global convergence guarantees. FGD and similar procedures are widely used in practice for problems that can be posed as matrix factorization. To the best of our knowledge, this is the first paper to provide precise convergence rate guarantees for general convex functions under standard convex assumptions.

Gaussian processes allow for flexible specification of prior assumptions of unknown dynamics in state space models. We present a procedure for efficient Bayesian learning in Gaussian process state space models, where the representation is formed by projecting the problem onto a set of approximate eigenfunctions derived from the prior covariance structure. Learning under this family of models can be conducted using a carefully crafted particle MCMC algorithm. This scheme is computationally efficient and yet allows for a fully Bayesian treatment of the problem. Compared to conventional system identification tools or existing learning methods, we show competitive performance and reliable quantification of uncertainties in the model.

This paper addresses the problem of localizing audio sources using binaural measurements. We propose a supervised formulation that simultaneously localizes multiple sources at different locations. The approach is intrinsically efficient because, contrary to prior work, it relies neither on source separation, nor on monaural segregation. The method starts with a training stage that establishes a locally-linear Gaussian regression model between the directional coordinates of all the sources and the auditory features extracted from binaural measurements. While fixed-length wide-spectrum sounds (white noise) are used for training to reliably estimate the model parameters, we show that the testing (localization) can be extended to variable-length sparse-spectrum sounds (such as speech), thus enabling a wide range of realistic applications. Indeed, we demonstrate that the method can be used for audio-visual fusion, namely to map speech signals onto images and hence to spatially align the audio and visual modalities, thus enabling to discriminate between speaking and non-speaking faces. We release a novel corpus of real-room recordings that allow quantitative evaluation of the co-localization method in the presence of one or two sound sources. Experiments demonstrate increased accuracy and speed relative to several state-of-the-art methods.

In this paper we consider the problem of data clustering under the union of subspaces (UOS) model [1], [2], when each data vector is sampled in an element-wise manner. This is referred to as the case of missing data. In other words we are looking to harvest a union of subspaces structure from the data, when the data is missing. Such a problem has been recently considered in a number of papers [3], [4], [5], [6]. This setting has implications to data completion under the union of subspaces model in contrast to the single subspace model that has been prevalent in the matrix completion literature. In contrast to statistical analysis in [3], [4], [5], this paper uses a variant of the sparse subspace clustering (SSC) algorithm [2] to give sufficient deterministic conditions for accurate subspace clustering under missing data. In contrast to [6], which does not provide any specific conditions for success of SSC under missing data, in this paper we provide implications of the deterministic conditions for several specific cases of sampling. Further through extensive simulations we demonstrate for the first time that accurate clustering under missing data does not imply accurate subspace clustering and completion thereby indicating the natural order of hardness of these problems under missing data.

Let's get started with lesson three of our Practicing Deep Learning Series. So far our focus has been on a very simple network comprised of a single neuron. Though we've discussed its parts, we have neglected to show it actually doing anything. The focus of part three is to start diving into some actual code to illustrate the simple network we've discussed. We will spend a fair amount of time on the single neuron network so that you can get familiar with Keras while gaining an understanding of the basics of a simple network. As soon as this is complete, we will be moving onto multilayer networks, which are much more powerful than the simple networks below.

Machine learning is, to keep it simple, an algorithm developed to note changes in data and evolve in it's design to accommodate the new findings. As applied to predictive analytics, this feature has wide ranging impact on the activities normally undertaken to develop, test, and refine an algorithm for a given purpose. Sophisticated pattern recognition – Along with noting relationships, the Yottamine Predictive Platform can determine the type and quantify as well. This is not just happening with key, or even secondary variables, but on every relationship that takes part in the pattern. This feature delineates irrelevant data as well, which provides the benefits of mitigating pre-processing requirements and accelerating processing.